In a saucepan, cover the chickpeas with water. Add the carrot, celery, onion, fennel, garlic, thyme, bay leaf, and 1/4 cup of the olive oil. Bring to a simmer, cover and cook over low heat until the chickpeas are tender, about 1 hour. Let the chickpeas cool in the liquid to room temperature, then drain, reserving 3/4 cup of the cooking liquid. Discard the vegetables and herbs.

Set aside 1/2 cup of the chickpeas. In a food processor, puree the remaining chickpeas with the reserved 3/4 cup of cooking liquid, and the remaining 1/4 cup of oil. Season with salt and pepper. Scrape the puree into a large bowl, stir in the parsley, preserved lemon peel, lemon juice, and the reserved 1/2 cup of chickpeas, and serve.